I use Hostgator and I'm having the same problem.
Internet Explorer and Edge have no problem. Firefox and Chrome do.
It's not just read and unread messages. It's last post, and new posts not showing up in threads, and even the time.
It's caused by Firefox not recognizing that the page has changed, and Firefox is loading from its cache. If you click the reload button in Firefox, everything is corrected, but ONLY for THAT PAGE, that one instance. You have to reload EVERY page, every time you go to that page.
You can go to my page:
http://www.chronologyproject.com/phpbb2/
and check the board time. Spend a couple of minutes browsing through threads, and then return to the main forum page. It still shows the old time. Click the refresh/reload button, and everything's fine.
I have tried:
Clearing the browser's cache.
Clearing the forum's cache.
Changing the forum's cookie name.
Chrome is having additional problems with logging people out. At first I thought it was a problem with a new version of Firefox, since I hadn't changed anything, and Firefox pushed out an update earlier this week. But with further problems with Chrome, and the apparent common denominator of Hostgator, I'm looking at them. Can anyone provide any thoughts as to what we need to say to Hostgator?